Ionic radius

Meaning of ionic radius

Ionic radius is a structural model

In a crystal, neighbouring ions do not meet at perfectly sharp surfaces. Diffraction experiments determine distances between nuclei, and a radius scheme partitions those distances into effective ionic contributions. Different schemes can assign somewhat different values because the partition is a model.

This is why a quoted ionic radius should be read together with the ion’s oxidation state and coordination number. A six-coordinate Fe²⁺ value should not be compared casually with a four-coordinate Fe²⁺ value as though both describe one immutable sphere.

Removing electrons usually makes a cation smaller

When an atom forms a cation, electron–electron repulsion decreases while the nuclear charge is unchanged. If ionization removes the entire outer shell—as when Na becomes Na⁺—the size change is especially large because the highest occupied principal shell disappears.

Higher positive charge on the same element generally pulls the remaining electrons inward more strongly. Fe³⁺ is therefore smaller than Fe²⁺ in comparable coordination environments.

Adding electrons usually makes an anion larger

Adding electrons to form an anion increases electron–electron repulsion in the valence region while nuclear charge remains fixed. The cloud expands until attraction to the nucleus and repulsion among electrons reach a new balance.

For the same element, a more negative charge therefore usually means a larger radius when comparable states exist. The general logic is the opposite of cation formation: more electrons share the same nuclear attraction.

What controls ionic size

Isoelectronic series give the cleanest comparison

O²⁻, F⁻, Na⁺, Mg²⁺ and Al³⁺ each contain 10 electrons. Because electron number and broad configuration are held constant, the main changing variable is nuclear charge. The radius decreases strongly as proton number rises.

Coordination number changes tabulated ionic radius

An ion surrounded by four neighbours is embedded in a different geometry from the same ion surrounded by six or eight neighbours. Effective radii derived from crystal structures therefore depend on coordination number. Higher coordination commonly corresponds to a larger tabulated radius because the ion participates in longer average contacts.

For structural chemistry, this is not a nuisance—it is useful information. The radius value records how the ion behaves in a particular local environment.

Oxidation state changes size within the same element

Increasing positive oxidation state generally decreases cation radius. Removing more electron density reduces repulsion and increases the attraction per remaining electron. This is why Fe³⁺ is smaller than Fe²⁺ and why high-charge transition-metal ions often have strong electric fields around them.

The effect matters in crystal structures, hydration and ligand binding. A small, highly charged ion can pull strongly on neighbouring electron density and distort otherwise simple ionic pictures.

Chemical consequences of ionic size

Charge density connects radius to polarization

A cation’s ability to polarize a neighbouring anion grows when the cation is small and highly charged. This is the basis of the qualitative ideas often associated with Fajans’ rules. Li⁺, for example, is much smaller and more polarizing than Cs⁺.

As polarization grows, bonding can acquire more covalent character. Ionic radius therefore connects geometrical size to the continuum between idealized ionic and covalent bonding.

Periodic trends need separate cation and anion comparisons

Down a group, ionic radii generally increase because an additional electron shell is occupied. Across a period, however, the pattern is interrupted when the common ion charge changes. Comparing Na⁺, Mg²⁺ and Al³⁺ is meaningful because they are isoelectronic; jumping directly from a small cation to a large anion across the same row creates a discontinuity.

Transition metals add another complication because several oxidation states are common. A radius trend is meaningful only after charge state and coordination are specified.

Hydration and lattice energy make ionic size chemically visible

Size changes the electric field around an ion. A small ion with the same charge places that charge into a smaller volume and interacts more strongly with nearby dipoles or counter-ions. This is why Li⁺ is hydrated more strongly than K⁺ in water and why Mg²⁺ produces a much stronger local electric field than a large singly charged cation.

In ionic solids, shorter cation–anion distances generally strengthen electrostatic attraction and can increase lattice energy when the charges are comparable. Radius therefore influences melting behaviour, solubility and structural preference indirectly through electrostatics.

The comparison still needs context. Solvation, entropy, covalency and crystal packing can oppose a simple radius-based expectation, so “smaller ion = stronger lattice” is a mechanism to consider rather than a complete prediction.

Ionic radius is not an isolated predictor of crystal structure

Radius ratios can help rationalize coordination in ionic solids, but real structures reflect more than geometry. Charge, polarization, directional covalency, lattice energy, electronic structure and temperature can all matter. A radius-ratio rule is therefore a model, not a universal law.

The most reliable use of ionic radii is comparative: choose values from the same radius set, same oxidation state conventions and compatible coordination environments, then connect the size difference to a structural or energetic question.

Exercises

Isoelectronic ranking

Order O²⁻, F⁻, Na⁺ and Mg²⁺ from largest to smallest radius.

Iron ions

Which is expected to be smaller in comparable coordination, Fe²⁺ or Fe³⁺?

Using a radius table

A table gives different radii for six-coordinate and eight-coordinate Ca²⁺. Is one value wrong?